Quoted:
Would a single pass through the dehumidifier bring the humidity down to an acceptable (45-60%) level?
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There really isn't a specific answer to that question - It'll depend on the type and size of the dehumidifier you use, fan speed, initial humidity level, etc., etc., etc.
Most dehumidifiers are little more than glorified air conditioners, complete with compressor, evaporator, condensor, fans, etc. - Which means that they ain't energy-stingy. You might end up spending as much operating your dehumidifier as you save by capturing greenhouse heat.
Personally, I like some humidity in my winter time heat - helps prevent cracked skin and lips, nosebleeds, respiratory infections, dry nose and mouth, etc. - and many folks install humidifiers in their heating systems specifically for this purpose.
So...why not try your heating scheme first without a dehumidifier ? You might be pleasantly surprised.